The International Society for Rock Mechanics and Rock Engineering (ISRM) recommends to use the ISRM Suggested Methods (SM) to avoid problems during tests. In any case, fulfilling SM requirements does not ensure a proper result each time they are applied due to the natural variability of the rocks. Between others, there are some requirements regarding the characteristics of the end surfaces of cylindrical specimens destined to be tested in compression strength tests: “They shall be flat to 0.02 mm, and shall not depart from perpendicularity of the specimen by more than 0.001 radian or 0.05 mm in 50 mm” (ISRM 2007). These requirements are achieved if a grinding machine is properly used after core cutting. Regretfully, such kind of machines, are usually medium sized and expensive equipment. Some rock mechanics laboratories usually rule out this grinding equipment due to a variety of reasons. This paper presents an introductory study that brings to light the necessity of having a grinding equipment. The results indicate that there is a clear decrease in strength when non-ground specimens are tested. On the other hand, the elastic parameters of the tested rock do not seem to be affected by grinding.